@KeithBeller的回答略有变化的变量名称和一些评论。

    public static void Main(string[] args)
    {
        List<int> input = new List<int>() { 3, 9, 8, 4, 5, 7, 10 };
        int targetSum = 15;
        SumUp(input, targetSum);
    }

    public static void SumUp(List<int> input, int targetSum)
    {
        SumUpRecursive(input, targetSum, new List<int>());
    }

    private static void SumUpRecursive(List<int> remaining, int targetSum, List<int> listToSum)
    {
        // Sum up partial
        int sum = 0;
        foreach (int x in listToSum)
            sum += x;

        //Check sum matched
        if (sum == targetSum)
            Console.WriteLine("sum(" + string.Join(",", listToSum.ToArray()) + ")=" + targetSum);

        //Check sum passed
        if (sum >= targetSum)
            return;

        //Iterate each input character
        for (int i = 0; i < remaining.Count; i++)
        {
            //Build list of remaining items to iterate
            List<int> newRemaining = new List<int>();
            for (int j = i + 1; j < remaining.Count; j++)
                newRemaining.Add(remaining[j]);

            //Update partial list
            List<int> newListToSum = new List<int>(listToSum);
            int currentItem = remaining[i];
            newListToSum.Add(currentItem);
            SumUpRecursive(newRemaining, targetSum, newListToSum);
        }
    }'

这也可以用来打印所有的答案

public void recur(int[] a, int n, int sum, int[] ans, int ind) {
    if (n < 0 && sum != 0)
        return;
    if (n < 0 && sum == 0) {
        print(ans, ind);
        return;
    }
    if (sum >= a[n]) {
        ans[ind] = a[n];
        recur(a, n - 1, sum - a[n], ans, ind + 1);
    }
    recur(a, n - 1, sum, ans, ind);
}

public void print(int[] a, int n) {
    for (int i = 0; i < n; i++)
        System.out.print(a[i] + " ");
    System.out.println();
}

时间复杂度是指数级的。2^n的阶

我将c#示例移植到Objective-c，并没有在响应中看到它:

//Usage
NSMutableArray* numberList = [[NSMutableArray alloc] init];
NSMutableArray* partial = [[NSMutableArray alloc] init];
int target = 16;
for( int i = 1; i<target; i++ )
{ [numberList addObject:@(i)]; }
[self findSums:numberList target:target part:partial];


//*******************************************************************
// Finds combinations of numbers that add up to target recursively
//*******************************************************************
-(void)findSums:(NSMutableArray*)numbers target:(int)target part:(NSMutableArray*)partial
{
    int s = 0;
    for (NSNumber* x in partial)
    { s += [x intValue]; }

    if (s == target)
    { NSLog(@"Sum[%@]", partial); }

    if (s >= target)
    { return; }

    for (int i = 0;i < [numbers count];i++ )
    {
        int n = [numbers[i] intValue];
        NSMutableArray* remaining = [[NSMutableArray alloc] init];
        for (int j = i + 1; j < [numbers count];j++)
        { [remaining addObject:@([numbers[j] intValue])]; }

        NSMutableArray* partRec = [[NSMutableArray alloc] initWithArray:partial];
        [partRec addObject:@(n)];
        [self findSums:remaining target:target part:partRec];
    }
}

Java解决方案的Swift 3转换(by @JeremyThompson)

protocol _IntType { }
extension Int: _IntType {}


extension Array where Element: _IntType {

    func subsets(to: Int) -> [[Element]]? {

        func sum_up_recursive(_ numbers: [Element], _ target: Int, _ partial: [Element], _ solution: inout [[Element]]) {

            var sum: Int = 0
            for x in partial {
                sum += x as! Int
            }

            if sum == target {
                solution.append(partial)
            }

            guard sum < target else {
                return
            }

            for i in stride(from: 0, to: numbers.count, by: 1) {

                var remaining = [Element]()

                for j in stride(from: i + 1, to: numbers.count, by: 1) {
                    remaining.append(numbers[j])
                }

                var partial_rec = [Element](partial)
                partial_rec.append(numbers[i])

                sum_up_recursive(remaining, target, partial_rec, &solution)
            }
        }

        var solutions = [[Element]]()
        sum_up_recursive(self, to, [Element](), &solutions)

        return solutions.count > 0 ? solutions : nil
    }

}

用法:

let numbers = [3, 9, 8, 4, 5, 7, 10]

if let solution = numbers.subsets(to: 15) {
    print(solution) // output: [[3, 8, 4], [3, 5, 7], [8, 7], [5, 10]]
} else {
    print("not possible")
}

Javascript版本:

function subsetSum(numbers, target, partial) { var s, n, remaining; partial = partial || []; // sum partial s = partial.reduce(function (a, b) { return a + b; }, 0); // check if the partial sum is equals to target if (s === target) { console.log("%s=%s", partial.join("+"), target) } if (s >= target) { return; // if we reach the number why bother to continue } for (var i = 0; i < numbers.length; i++) { n = numbers[i]; remaining = numbers.slice(i + 1); subsetSum(remaining, target, partial.concat([n])); } } subsetSum([3,9,8,4,5,7,10],15); // output: // 3+8+4=15 // 3+5+7=15 // 8+7=15 // 5+10=15

function solve(n){
    let DP = [];

     DP[0] = DP[1] = DP[2] = 1;
     DP[3] = 2;

    for (let i = 4; i <= n; i++) {
      DP[i] = DP[i-1] + DP[i-3] + DP[i-4];
    }
    return DP[n]
}

console.log(solve(5))

这是JS的一个动态解决方案，告诉任何人有多少种方法可以得到一定的总和。如果考虑到时间和空间的复杂性，这可能是正确的解决方案。